# How do you divide (x^2+5x+1)div(x+3) using synthetic division?

Jan 20, 2018

color(magenta)((x^2+5x+1) / (x+3) = x+2 and remainder of color(magenta)(-5/(x+3)

#### Explanation:

$\textcolor{w h i t e}{a a a a}$$- 3$$\textcolor{w h i t e}{a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$1$$\textcolor{w h i t e}{a a a a}$$5$$\textcolor{w h i t e}{a a a a a}$$1$$\textcolor{w h i t e}{a a a a a a}$$\textcolor{w h i t e}{a a a a a a}$

$\textcolor{w h i t e}{a a a a a a}$$\textcolor{w h i t e}{a a a a a}$$|$$\textcolor{w h i t e}{a a a}$$\textcolor{w h i t e}{a a a a}$$- 3$$\textcolor{w h i t e}{a a a a}$$- 6$$\textcolor{w h i t e}{a a a a a}$$\textcolor{w h i t e}{a a a a a a}$

$\textcolor{w h i t e}{a a a a a a a a a a}$---------------------------------------------

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a}$$\textcolor{w h i t e}{a a a a a a}$$1$$\textcolor{w h i t e}{a a a a a}$$2$$\textcolor{w h i t e}{a a a a a}$$\textcolor{w h i t e}{a}$$- 5$$\textcolor{w h i t e}{a a a a a a}$

The remainder is color(magenta)(=-5/(x+3)

The quotient is color(magenta)(=x+2